Playlist

Show Playlist

Hide Playlist

Ideal Gas Law

Blood is responsible for preventing the body from cooling down, while sweat prevents it from overheating. But how exactly does this work? Basic knowledge of thermodynamics is necessary in order to understand heat transfer, the functions of substance mixtures, and the relevance of different pressures inside the human body. What is a gas? What are the properties of different substances, and how can they be described? The following article deals with these basic principles of physics.

Gases are one of the phases of matter where the particles are vastly separated unlike what takes place in solids and liquids where particles are closer together. Gases are hard to observe so they are classified according to temperature, a number of particles, pressure, and volume.

00:01
Now that we have an idea of how to derive some of the basic lawsand how these are come up with experimentally, certain proportionalities.
00:08
We're ready to derive one all-encompassing lawthat incorporates all the laws we just discussed.
00:14
And that's the ideal gas law.
00:16
What we do with the ideal gas lawis take the laws that we just came up with which are here.
00:21
These experimental results are giving a certain proportionalitiesand try to put all the variables that we discussed into one equation.
00:28
If we do that, we could say that the pressure times the volumeis proportional to the number, the number of moleculestimes the temperature of your system.
00:37
This satisfies as you can tell by examinationand I do recommend that you look at this and really think about it and seehow the ideal gas law actually matchesand would give you all of these individual experimental results that we found already.
00:51
We could then ask ourselves if it's proportional to the pressuretimes the volume is proportional to the number of particles times there temperature.
00:59
What is the proportionality constant?In other words, I know that if I double the pressure,I will have doubled the number times the temperature.
01:07
But I don't know what the actual numbers are,so I would like to know what this proportionality constant is.
01:13
It turns out and you can find this experimentallythat is proportionality constant is a number called Rand this number is called the universal gas constant.
01:23
It has a value of a little more than 8 joules per Kelvin moleand you can always look at the unit yourself to make surethat the left-hand side of the equationand the right-hand side of the equation have the same units.
01:35
When we're giving a constant values,here's how you would solve a problem using the ideal gas law.
01:42
So we've listed one more time the ideal gas law above,pressure times volume equals number times the gas constant times temperature,PV equals nRT.
01:51
You take particular constant values in a problemso most problems you could assume some things are constant,either because that's told to you or because you can infer on your own.
02:00
What you do is simply collect all those constants together mathematicallyand then everything that's left on the other side of your equationmust be conserved because they're equal to a constant.
02:10
Just to give this a concrete example and make sure it makes some sense.
02:15
Suppose we had a constant volume and temperature in some given problem.
02:19
What we could do is re-arrange the ideal gas lawso that we have all of our constants together in this case the temperatureand the volume are constant and the gas constantis of course by definition of constant so if we put all these together,we have something like this, R times T divided by the volume.
02:37
Everything else in the gas law which is now just P over nis clearly just mathematically equal to a constant.
02:45
Which means that P over n, the pressure over the number of particlesis conserved because it's a constant.
02:51
Which means that in a given problem,we can take the initial pressure and numberand relate it to the final pressure and numberbecause this ratio as we just saw has to be some constant value.
03:03
There's one other way the gas law is writtenso it's good to go over that and see where it comes fromand how it relates to the gas law that we've just derived.
03:11
What you can notice is that if we look at the right-hand side of the gas law here.
03:15
We can look at that, that quantity,the number times that gas at a constant.
03:20
The number in units, so let's look at the units of this,we have the number of moles times the gas constant which is joules per Kelvin mole.
03:29
Instead of measuring in moles what we could dois instead actually measure the number of molecules.
03:35
So cancelling the units of moles or re-writing in terms of number of moleculeswe could say that we have instead the number of moleculestimes a new constant and that constant is called K.
03:45
K is Boltzmann's constant and instead has units of joules per Kelvinrather than joules per Kelvin mole like the universal gas constant did.
03:57
Sometimes this is called the microscopic form of the ideal gas lawbecause instead of measuring moles which again is a very big number.
04:04
It is the way to measure, you know actual physical quantitiesthat you might scoop up from the ground.
04:08
We're actually measuring the number of molecules there at themselvesand so this microscopic form of the ideal gas lawis better suited the case as what we're talking aboutparticular interactions and actually counting the number of molecules.
04:22
There's a few ways to describe how this law is derive.
04:25
So here's one more that might help you if it makes more sense.
04:28
We can just look at that term R times T and compare it to the term K times T.
04:34
Again the only difference is that in one case we're taking the number of molesand multiplying by joules per mole.
04:40
And then the other case we're taking the number of moleculesand multiplying by joules per molecule.
04:46
So again you get the same numberseverything else in the ideal gas law is the same.
04:51
There's no actual difference if you were doing a problem.
04:53
It's just a different way of measuring the number of molecules or the number of moles,in whatever system that you have.

About the Lecture

The lecture Ideal Gas Law by Jared Rovny is from the course Gas Phase.

Included Quiz Questions

Which of the following indicate the ideal gas law?

P∝nT/V

P∝nV/T

P∝R

P∝nTV

P∝(VT)/n

According to the ideal gas law, which of the following quantities must remain constant if you hold the pressure and particle number constant?

T/V

T

V

TV

T+V

In the expressions of the ideal gas law, what is the difference between n and N?

n expresses number in moles, while N expresses number in molecules

n expresses number in molecules, while N expresses number in moles

n expresses number in density, while N expresses the number of molecules

n expresses the number of molecules, while N expresses number in density

n expresses number per volume, while N expresses number in total

Author of lecture Ideal Gas Law

Jared Rovny

Customer reviews

(1)
5,0 of 5 stars

5 Stars

5

4 Stars

0

3 Stars

0

2 Stars

0

1 Star

0

User Reviews

(1)
5,0 of 5 stars

5 Stars

5

4 Stars

0

3 Stars

0

2 Stars

0

1 Star

0

Subscribe to bookmark your content

Bookmarks will help you organize our more than 2000 medical videos,
and customize your learning experience for more efficiency and better results.

USMLE™ is a joint program of the Federation of State Medical Boards
(FSMB®) and National Board of Medical Examiners (NBME®). MCAT is a registered
trademark of the Association of American Medical Colleges (AAMC).
None of the trademark holders are endorsed by nor affiliated with Lecturio.